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Percolation and Internet Science

Author

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  • Franco Bagnoli

    (Department of Physics and Astronomy and CSDC, University of Florence, via G. Sansone 1, 50019 Sesto Fiorentino, Italy
    INFN, sez. Firenze, via G. Sansone 1, 50019 Sesto Fiorentino, Italy)

  • Emanuele Bellini

    (Centre on Cyber-Physical Systems (C2PS), Khalifa University, Saada Street, P.O. Box 127788, Abu Dhabi, United Arab Emirates)

  • Emanuele Massaro

    (HERUS Lab, École Polytechnique Fédérale de Lausanne (EFPL), GR C1 455 (Bâtiment GR)—Station 2, CH-1015 Lausanne, Switzerland
    ISI Foundation, via Chisole 5, 10126 Torino, Italy)

  • Raúl Rechtman

    (Instituto de Energás Renovables, Universidad Nacional Autónoma de México, Temixco 62580, Mexico)

Abstract

Percolation, in its most general interpretation, refers to the “flow” of something (a physical agent, data or information) in a network, possibly accompanied by some nonlinear dynamical processes on the network nodes (sometimes denoted reaction–diffusion systems, voter or opinion formation models, etc.). Originated in the domain of theoretical and matter physics, it has many applications in epidemiology, sociology and, of course, computer and Internet sciences. In this review, we illustrate some aspects of percolation theory and its generalization, cellular automata and briefly discuss their relationship with equilibrium systems (Ising and Potts models). We present a model of opinion spreading, the role of the topology of the network to induce coherent oscillations and the influence (and advantages) of risk perception for stopping epidemics. The models and computational tools that are briefly presented here have an application to the filtering of tainted information in automatic trading. Finally, we introduce the open problem of controlling percolation and other processes on distributed systems.

Suggested Citation

  • Franco Bagnoli & Emanuele Bellini & Emanuele Massaro & Raúl Rechtman, 2019. "Percolation and Internet Science," Future Internet, MDPI, vol. 11(2), pages 1-26, February.
    • Handle: RePEc:gam:jftint:v:11:y:2019:i:2:p:35-:d:203182
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    References listed on IDEAS

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    1. Adler, Joan, 1991. "Bootstrap percolation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 171(3), pages 453-470.
    2. Dorogovtsev, S.N. & Mendes, J.F.F., 2003. "Evolution of Networks: From Biological Nets to the Internet and WWW," OUP Catalogue, Oxford University Press, number 9780198515906.
    3. Isham, Valerie & Harden, Simon & Nekovee, Maziar, 2010. "Stochastic epidemics and rumours on finite random networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(3), pages 561-576.
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    Cited by:

    1. Vispoel, Milan & Daly, Aisling J. & Baetens, Jan M., 2024. "Damage spreading and the Lyapunov spectrum of cellular automata and Boolean networks," Chaos, Solitons & Fractals, Elsevier, vol. 184(C).

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